The present invention relates to the determination of concentration of antibodies or precipitate-forming antigens present in a wide variety of samples, and more particularly, to such determination by nephelometric means.
Specific antigens may be detected by means of their reaction with corresponding antibodies. For example, polyvalent protein antigens may react with their respective antibodies to produce a precipitate which forms in such a way that the amount of precipitate is proportional to either the antibody concentration or the antigen concentration, depending on which is present in excess. Such antibodies are called "precipitins", and their reactions are "immuno-precipitin reactions". As stated, in these reactions, the amount of precipitate is proportional to either the antibody concentration or the antigen concentration, depending on which is present in excess, as shown in FIG. 1. For example, if the antibody is present in excess, the quantity of precipitate formed is related to the concentration of antigen in the sample. On the other hand, if excess antigen is present, the quantity of precipitate is related to the concentration of antibody. For purposes of discussing the prior art and background of the invention and, later, for setting forth the present invention, the analysis of antigen in sera during antibody excess will be used. It is to be understood that this convention is adopted for ease of discussion and is not intended to limit the scope of the invention as set forth herein.
The combination of antigen with antibody is a specific yet reversible chemical reaction. Since its discovery, the precipitin reaction has been used extensively as a qualitative or semi-quantitative technique for estimating either antigen or antibody concentrations. Generally, this is accomplished by allowing the reaction to go to completion and centrifuging or filtering the precipitate formed. Under optimal conditions, the reaction occurs rather rapidly, and precipitation may be complete within a time period of only a few minutes. Under more typical conditions, the precipitation requires intervals of as long as several hours, or even a number of days, depending on other solution characteristics such as ionic strength, salt species present, and the presence of other hydrophobic or hydrophilic macro-molecules.
When the reaction is allowed to go to completion, the amount of protein precipitated for a given amount of antibody increases with the amount of polyvalent antigen up to a maximum, beyond which larger amounts of the antigen lead to progressively less precipitation. Thus the quantity of precipitate formed in an antigen-antibody reaction depends on the relative concentrations of the two reactants. The curve of FIG. 1 describes the quantity of precipitate formed, as a function of the antigen concentration in the reaction mixture, for a given antibody concentration. It may be seen that there are three distinct zones in the curve of antigen concentration versus quantity of precipitate formed. On the ascending limb of the curve, the antibody is present in excess. On the descending limb of the curve, the antigen species is present in excess. The region of maximum precipitation is called the equivalence point with matching concentrations of antigen and antibody.
Most antibody molecules are bivalent, while the precipitating antigens are multivalent. These reactants combine in a series of consecutive reactions which may be summarized in the following steps:
(1) Primary interaction of association, with formation of a binary antigen-antibody complex; PA1 (2) Lattice formation through reaction of the primary complexes leading to the formation of larger complexes consisting of a lattice of antigen and antibody molecules; PA1 (3) Aggregation of these lattice-like complexes to form the visible precipitate.
The specific structure of the stable lattice achieved with the bivalent antibody and multivalent antigen is still unknown, since the number of possibilities is large. There is, however, significant evidence for the formation of a stable lattice, and it is apparent that in the antibody excess region of the precipitin curve there is no free antigen detectable in the soluble phase after formation of the precipitate, although antibody is still present in the supernatant liquid. In the equivalence region, neither antigen nor antibody is found in the supernatant liquid, except perhaps in very small amount.
In the area of antigen excess, complex formation itself is a much simpler process. In this region little precipitation occurs because of the high probability that each antibody molecule will be bound to two antigen molecules, with subsequent lattice formation being impossible owing to the lack of free antibody valence. Precipitation, then, may be considered a consequence of the growth of antibody-antigen aggregates in such a way that each antigen molecule is linked to more than one antibody molecule, and, in turn, each antibody molecule is linked to more than one antigen molecule. When these aggregates exceed some critical volume they settle out of solution spontaneously due to the increase in sedimentation rate caused by the increase in the volume of the particle. Thus, if the lattice formed in Step 2 of the aforementioned mechanism is sufficiently large, as will tend to be the case near equivalence, precipitation will occur without the aggregation of adjacent lattices.
On the other hand, under conditions of antibody excess, the close packing of antibody molecules when bound to an antigen molecule provides opportunity for neighboring antibody molecules to react with one another through the formation of ionic bonds between oppositely charged groups. As a consequence, lattices consisting of large numbers of antibody molecules may become relatively hydrophobic and tend progressively to associate with one another and become increasingly insoluble. Thus in the condition of extreme antibody excess, corresponding to very low antigen concentrations, even though sufficiently large lattices to form precipitation may not occur, aggregation of small hydrophobic lattice elements consisting of low concentrations of antigen still give rise to a visible precipitate. This view is supported by an analysis of the effects of ionic strength on precipitation and by experiments concerning the advancement of precipitation. In the former, increasing salt concentrations cause increasing precipitation. In the latter, the addition of hydrophilic agents or species were found to increase the effective hydrophobicity of the precipitating species. Thus, it may be seen that at a very low antigen concentration a visible precipitate may be formed through the third step, but not through the second step, in the aforementioned mechanism. Accordingly, at such low antigen concentrations, the relationship between quantity of precipitate formed and concentration of the antigen molecule is extremely nonlinear.
Once a precipitin curve has been constructed for a known antibody and its respective antigen, the antiserum can be used to measure the concentration of that antigen in an unknown sample. The assay for antigen is carried out in the antibody excess region (except for that very low antigen concentration region discussed above), since that is the region where precipitation is quantitatively related to the amount of antigen. Throughout the range from an antigen concentration of zero up to the equivalence point, all of the available antigen in the unknown sera will be complexed by the excess antibody and will be precipitated, making the precipitin reaction an extremely good quantitative tool. In fact, extreme specificity is provided if the antiserum is free of extraneous antibodies that could precipitate with other antigens in the test sample solution. Quantification of antigens in this way is ambiguous, however, since a given quantity of precipitate may imply one value of antigen concentration if the antibody is present in excess, while it may imply another value of antigen concentration if the antigen is present in excess. That is to say, a given amount of precipitate formed in an antibody/antigen reaction may correspond to two values of antigen concentration, depending on which of the two species, antibody or antigen, is present in excess. With unknown samples, the latter fact is often in question.
Methodologies presently exist for quantifying precipitate-forming antigens or antibodies in solution by analyzing precipitates formed upon their reaction with their specific immunochemical partners. Most commonly, the amount of precipitate formed is measured by measuring the amount of light scattered from a beam of light passing through the solution. In general, the procedure involves the addition of the antigen containing sample to an antibody solution and a buffer. The solution is then allowed to incubate over the period of time necessary for the antigen and antibody to react completely. Upon complete reaction, the solution is placed in a measuring cell. A beam of collimated light then is passed through the cell and the amount of light scattered perpendicularly to the direction of the incident light is measured to produce a "nephelometric signal". By graphic analysis using a series of standard curves, the value of the nephelometric signal is converted to a measure of antigen concentration in the sample solution. In this regard, the standard curves are developed by graphically plotting the value of nephelometric signals generated from reactions of standard antigen solutions of various dilutions (in saline) with reagents of known antibody concentrations. The graphic analysis involves operating with the standard curve derived under the same antigen, dilution, and reagent concentration conditions as those under which a sample solution was tested to generate the nephelometric signal. Specifically, the value of the nephelometric signal is graphically noted on the abscissa for the selected standard curve and a corresponding value noted for antigen concentration on the ordinate for the selected standard curve. The noted value of antigen concentration is the concentration of antigen in the sample solution if the sample has been measured under conditions of antibody excess as previously described.
Nephelometric methods afford a convenient means for monitoring immuno-precipitin reactions at an early stage in the reaction. As the reaction proceeds, the initial 1:1 complexes grow to form larger units which increasingly scatter light prior to the separation of a precipitate. Given sufficient time, particles large enough to precipitate will be formed. Significantly increased light scattering is observed, however, before the larger units become sufficiently agglomerated to settle out. Thus, the term "scattering centers" rather than "particles" or "precipitate" is more accurately used to describe the product measured by nephelometric techniques.
The formation of the larger complexes in a free solution medium can be accelerated by the presence of hydrophilic agents which tie up a significant fraction of the water, thus enhancing the probability of protein-protein interaction. The most widely used of these hydrophilic agents is polyethyleneglycol (PEG) with an average molecular weight of 6000. In the presence of about 40 g/1 PEG 6000, the build-up of complexes of sufficient size to give a level of light-scatter adequate for quantitative measurement occurs in a time interval of tens of seconds, and the maximum scatter level is reached within a few minutes, as opposed to 30-90 minutes in the absence of PEG. The short reaction time obtained in the presence of PEG makes possible the rapid direct measurement of precipitating antigens, by means of measuring the increase of light scattered by the larger units formed from the primary antigen-antibody complexes.
The nephelometric approach, as contrasted to procedures in which the precipitate is physically separated from the clear solution for measurement, affords a means for observing the immuno-precipitin reaction under dynamic conditions -- i.e., while it is taking place. The initial 1:1 complexes generally are too small to scatter visible light to a significantly greater extent than do the separated components. Thus, only the secondary build-up of larger units which serve as scattering centers can be observed. However, the actual end point of an immuno-precipitin reaction is difficult to define. This is because the precipitate formed eventually tends to settle out from the solution thereby decreasing the light scatter at a time when scatter should otherwise be maximal. The observed scatter is thus dependent both on the amount of material and on the state of its dispersion within the measuring cell. It is therefore preferable to make nephelometric measurements under dynamic conditions, rather than waiting for the reaction to go to completion.
Instead of waiting for the reaction to be complete before measuring the nephelometric signal, the nephelometric signal can be measured beginning at the time when the antigen and the antibody are brought into contact in solution. In such case, it is found that the nephelometric signal develops to its final value over a period of time which may be as short as a few minutes or as long as several hours. During the development of the reaction, the nephelometric signal takes the form of a sigmoidal curve, beginning at some relatively low value, progressively increasing at an accelerating rate until at some point in time it undergoes an inflection and begins to decrease its time rate of change until the nephelometric signal asympotitically approaches its final value, as shown in FIG. 2. The first derivative of the nephelometric signal as a function of time is therefore roughly Gaussian in shape, as shown in FIG. 3. It develops a peak value at the inflection point, after which the increasing nephelometric signal begins to approach its asymptotic value. It has been determined that the time rate of change of the nephelometric signal at the inflection point is directly related to the final asymptotic value of the nephelometric signal. It is possible, therefore, to quantify the amount of immuno-precipitin reaction, by measuring the derivative of the nephelometric signal with respect to time, and quantifying the peak of the rate signal thus obtained. Under suitable conditions, a maximum or "peak" rate is obtained within 10-40 seconds after introduction of the triggering reagent (antigen or antibody) to the reaction mixture.
The rate of change of the nephelometric signal has been proposed in the quantification of specific protein antigens in sera as set forth in the following publications: (1) Specific Protein Analysis by Light-Scatter Measurement with a Miniature Centrifugal Fast Analyzer, T. O. Tiffany, J. M. Parella, W. F. Johnson, and C. A. Burtis, Clinical Chemistry, Vol. 20, No. 8 (1974), p. 1055; (2) Kinetics of the IgG Anti-IgG Reaction, as Evaluated by Conventional and Stopped-Flow Nephelometry, John Savory, Gregory Buffone, and Richard Reich, Clinical Chemistry, Vol. 20, No. 8 (1974), p. 1071; (3) Use of a Laser-Equipped Centrifugal Analyzer for Kinetic Measurement of Serum IgG, Gregory J. Buffone, John Savory, and R. E. Cross, Clinical Chemistry, Vol. 20, No. 10 (1974), p. 1320; and (4) Evaluation of Kinetic Light Scattering as an Approach to the Measurement of Specific Proteins with the Centrifugal Analyzer. I. Methodology, Gregory J. Buffone, John Savory, R. E. Cross, and J. E. Hammond, Clinical Chemistry, Vol. 21, No. 12 (1974) p. 1731.
When considering the prior art, however, it is important to ascertain the way in which the particular authors are using the term "rate". In particular, the term "rate" is often used in place of intensity when referring to the nephelometric signal. In that regard, the instantaneous rate of production of precipitate is directly related to the quantity of precipitate and, therefore, the intensity of the nephelometric signal. Such uses of the term "rate" to indicate intensity are common in publications (2), (3) and (4) above. For example, in publication (2) at page 1074, FIG. 7 is titled "Rate of change of light scattering in polyethylene glycol". Inspection of the Figure, however, discloses a coordinate system labeled "relative intensity" and "time" while the curve itself is the classic sigmoidal curve characteristic of the nephelometric intensity signal. By contrast, publication (1) uses rate in its proper manner, being the rate of change with respect to time of the nephelometric signal. It is in this manner that the term "rate" is used hereinafter to describe a novel approach to the determination of antibody/antigen excess in immunonephelometric analysis. The lack of such an improved method of determining antibody/antigen excess is noted in reference (2) wherein it states, "Detection of antigen excess is also an important factor in all immunoassay methods. Possibly a centrifugal analyzer system could be used to monitor early changes in reaction rates and provide a means by which low antigen concentration could be differentiated from very high antigen concentrations as seen in FIG. 4. " The detection of antigen excess and the equilibrium area is an even more serious problem as this is the environment of actual interest in immunoassay procedures as will be discussed in greater detail hereinafter. As will be seen, in simple excess situations as opposed to "high" excess situations an improved method of determining antibody/antigen excess is required before true rate analysis of a nephelometric signal can be usefully employed in the determination of protein concentrations. The present invention provides such an improved method and apparatus.
Previously, the rate of change of a nephelometric signal has been determined by a periodic sampling of the nephelometric signal. In particular, maximum change during such sampling periods has been determined by a sample and comparison method and, when found, the maximum value and next lower value have been used to calculate a slope or rate line directly related to the final protein concentration. The accuracy of such an approach is, of course, dependent on the sampling frequency. The shorter the period, the higher the probability that the sample will be taken during the period that the time rate of change of the nephelometric signal reaches a maximum. Under such circumstances, a reasonably accurate approximation of the maximum or peak rate probably will be obtained. However, when dealing with probabilities, there is also a considerable chance of error and incorrect determinations of final protein concentration. Further, such presently employed methods provide only an approximation of the elapsed time to the occurrence of peak rate and hence are rather inaccurate in their determination of antigen excess. Accordingly, even having determined peak rate, the present methods are inaccurate in determining which of the two possible concentration values it represents.
Therefore, it is the object of the present invention to provide a technique for establishing both concentration and antigen excess existence following a determination of the precise maximum rate and the exact time of occurrence of that maximum rate.